Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 3 (2019), 491-502.

On the preservation of properties by piecewise affine maps of locally compact groups

Serina Camungol, Matthew Morison, Skylar Nicol, and Ross Stokke

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As shown by Cohen (1960) and Ilie and Spronk (2005), for locally compact groups G and H , there is a one-to-one correspondence between the completely bounded homomorphisms of their respective Fourier and Fourier–Stieltjes algebras φ : A ( G ) B ( H ) and piecewise affine continuous maps α : Y H G . Using elementary arguments, we show that several (locally compact) group-theoretic properties, including amenability, are preserved by certain continuous piecewise affine maps. We discuss these results in relation to Fourier algebra homomorphisms.

Article information

Involve, Volume 12, Number 3 (2019), 491-502.

Received: 27 February 2018
Accepted: 9 September 2018
First available in Project Euclid: 5 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22D05: General properties and structure of locally compact groups 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A07: Means on groups, semigroups, etc.; amenable groups 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
Secondary: 20E99: None of the above, but in this section

locally compact group piecewise affine map amenability Fourier algebra


Camungol, Serina; Morison, Matthew; Nicol, Skylar; Stokke, Ross. On the preservation of properties by piecewise affine maps of locally compact groups. Involve 12 (2019), no. 3, 491--502. doi:10.2140/involve.2019.12.491.

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